Circling Vultures

When the ability resolves, you choose whether to sacrifice the creature or perform the other action. If you can't perform the other action, then you must sacrifice the creature.

If an effect or rule puts two or more cards into the same graveyard at the same time, the owner of those cards may arrange them in any order.

The "top" card of your graveyard is the card that was put there most recently.

Players may not rearrange the cards in their graveyards. This is a little-known rule because new cards that care about graveyard order haven't been printed in years.

If the creature is no longer on the battlefield when the ability resolves, you may still perform the action if you want.

Say you're the owner of both a permanent and an Aura that's attached to it. If both the permanent and the Aura are destroyed at the same time (by Akroma's Vengeance, for example), you decide the order they're put into your graveyard. If just the enchanted permanent is destroyed, it's put into your graveyard first. Then, after state-based actions are checked, the Aura (which is no longer attached to anything) is put into your graveyard on top of it.

The last thing that happens to a resolving instant or sorcery spell is that it's put into its owner's graveyard. —Example: You cast Wrath of God. All creatures on the battlefield are destroyed. You arrange all the cards put into your graveyard this way in any order you want. The other players in the game do the same to the cards that are put into their graveyards. Then you put Wrath of God into your graveyard, on top of the other cards.

Circling Vultures's discard ability is a static ability, not an activated ability. Although it acts like an activated ability that says "Discard Circling Vultures: Nothing happens," it is not one and cards like Pithing Needle or Abeyance won't prevent you from being able to discard it.